If I use very coarse mesh for the pre-deformation (such as pre-bending, gravity loading etc), and then refine the mesh in the later forming analysis. Will it result in obvious numerical error for the final results?

With coarse mesh, it is very efficient to obtain results for the
pre-deformation. However, if the mesh is too coarse, and there are big
differences between the neighboring element normals, then there might
cause unexpected artificial bending in the later deformations.

Even though the mesh can be refined after pre-deformation, the
newly added nodes will undergo further deformation to reach the curved
rigid body surface. Accordingly, there will be obvious difference
between the strains of neighboring elements, and there might cause
unexpected deformation localization along the edges of the adapted
elements.

It is not a good practice to have a too coarse mesh for the
pre-deformation if the curvature of the rigid tool is large. In other
words, the initial mesh should be based on the geometry of the rigid
tools.